There are situations where the same measurements are made from different samples, but there could be systematic differences among different sample means. Data fusion is an emerging area of research on combining information from multiple data sources to obtain improved parameter estimates. One way to borrow strength from other samples is to employ random effect models or multilevel models, which are parametric modeling approaches. This book introduces an alternative approach based on density ratio models (DRM). The DRM makes a parametric model assumption for the ratio of two density functions from two different samples, but the marginal distribution of the reference distribution is completely unspecified. Using the empirical likelihood method, parameters under DRM are efficiently estimated and likelihood ratio tests can also be developed. Thus, the DRM combined with empirical likelihood is regarded as a semiparametric approach to statistical data fusion. The book provides a comprehensive review of the DRM approach to data fusion. It is well written and easy to follow, although the technical details are not trivial. The authors did an excellent job in making a concise introduction of the statistical techniques in data fusion. The book contains several real data examples, and some R codes are also presented at the end of each chapter.
The DRM approach is extended to multivariate data, which is well described in Chapter 3. Chapter 4 covers some asymptotic properties of the proposed estimators for the parameters in the DRM. Some extension to “out of sample fusion” is introduced with examples in time series. I especially like Chapter 6 (Bayesian approach) and Chapter 7 (Small area estimation). Bayesian approach is useful in assessing the uncertainty of the DRM approach and can naturally incorporate prior information on the model parameters. I can see many potential research topics in this direction. Small area estimation in Chapter 7 is an important application of DRM to survey sampling. The DRM approach for small area estimation is quite new and seems to be a promising area of research.
I think the DRM is a powerful model for data fusion and many useful applications can be developed using DRM. Since the DRM is relatively new and there are no review articles on the subject, this book is a welcome addition to the literature. However, I find that several important topics are not covered. First, the model specification for DRM is not addressed. Second, it may not be realistic to assume that the samples have common support. How to handle such a problem can be practically important. Third, the choice of the weight function seems to be arbitrary and sensitivity analysis about the choice of the weight function is needed. Lastly, there is no comparison with the parametric model approach to data fusion. The above-mentioned topics may be important for practitioners who want to make the best use of multiple data sources. I hope such topics are covered in the second edition of the book.
Overall, I found that the book covers an important topic and the DRM is a promising tool in this area. Researchers on data fusion will surely find this book very helpful and I will use this book in studying with my Ph.D. students.